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Abstract We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean–Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics. 

A central focus of data science is the transformation of empirical evidence into knowledge. As such, the key insights and scientific attitudes of deep thinkers like Fisher, Popper, and Tukey are expected to inspire exciting new advances in machine learning and artificial intelligence in years to come. Along these lines, the present paper advances a novel {\em typicality principle} which states, roughly, that if the observed data is sufficiently ``atypical'' in a certain sense relative to a posited theory, then that theory is unwarranted. This emphasis on typicality brings familiar but often overlooked background notions like model-checking to the inferential foreground. One instantiation of the typicality principle is in the context of parameter estimation, where we propose a new typicality-based regularization strategy that leans heavily on goodness-of-fit testing. The effectiveness of this new regularization strategy is illustrated in three non-trivial examples where ordinary maximum likelihood estimation fails miserably. We also demonstrate how the typicality principle fits within a bigger picture of reliable and efficient uncertainty quantification. 

2D layered metal-organic frameworks (MOFs) are a new class of multifunctional materials that can provide electrical conductivity on top of the conventional structural characteristics of MOFs, offering potential applications in electronics and optics. Here, for the first time, we employ Machine Learning (ML) techniques to predict the thermodynamic stability and electronic properties of layered electrically conductive (EC) MOFs, bypassing expensive ab initio calculations for the design and discovery of new materials. Proper feature engineering is a very important factor in utilizing ML models for such purposes. Here, we show that a combination of elemental features, using generic statistical reduction methods and crystal structure information curated from the recently introduced EC-MOF database, leads to a reasonable prediction of the thermodynamic and electronic properties of EC MOFs. We utilize these features in training a diverse range of ML classifiers and regressors. Evaluating the performance of these different models, we show that an ensemble learning approach in the form of stacking ML models can lead to higher accuracy and more reliability on the predictive power of ML to be employed in future MOF research.